The memristor (“memory resistor”) was originally envisioned in 1971 by Leon Chua. Chua started by explaining the fundamental circuit elements: the resistor, capacitor, and inductor. Chua then proved that no combination of the other fundamental circuit elements (i.e., resistors, capacitors and inductors) could duplicate the properties of a memristor. This inability to duplicate the properties of a memristor with the other passive circuit elements makes the memristor another fundamental circuit element.
In 2008, a team at Hewlett-Packard (HP) Labs published the results of an analysis of a thin film of titanium dioxide made to behave as a memristor device. HP Labs went on to create an elementary circuit model that was defined by the same mathematical equations as those predicted by Chua for the memristor. The team then showed that this simple model could reproduce a wide variety of complex current-voltage (I-V) curves. The team also showed the equations for the drift of oxygen vacancies in titanium dioxide, and their influence on the electronic conduction in the material, were also identical with an equivalent circuit model, and thus the memristor equations.
From this, it was possible to develop a formula for the memristance of a device. This memristance formula showed that the size of the most important term in the memristance equations gets larger as the device size decreases. As such, understanding memristance is even more important as the size of circuits continue to get smaller. This is particularly true when designing electronic circuits in the realm of nano-size electronics.